What is the similarity between series and parallel resonance?

Explanation:

Series and Parallel Resonance in Electrical Circuits

Definition: Resonance in electrical circuits occurs when the inductive and capacitive reactances are equal in magnitude but opposite in phase, resulting in a purely resistive impedance at a specific frequency known as the resonant frequency. This phenomenon can happen in both series and parallel circuits.

Working Principle: In a resonant circuit, the inductive reactance (XL) and capacitive reactance (XC) cancel each other out at the resonant frequency (f_r). The resonant frequency is given by:

f_r = 1 / (2π√(LC))

where L is the inductance and C is the capacitance of the circuit.

At resonance, the impedance of the circuit is minimized in a series resonant circuit and maximized in a parallel resonant circuit. However, a key similarity between series and parallel resonance is that the power factor of the resonating circuit is unity (Option 2).

Advantages:

• High selectivity in filtering applications, allowing certain frequencies to pass while blocking others.
• Efficient energy transfer at the resonant frequency, making these circuits useful in applications such as wireless power transfer and RF communication.

Disadvantages:

• Resonant circuits can be sensitive to component variations, which may affect the resonant frequency.
• High currents or voltages at resonance can cause component stress or failure if not properly managed.

Applications: Resonant circuits are widely used in various applications, including radio receivers, filters, oscillators, and impedance matching networks.

Correct Option Analysis:

The correct option is:

Option 2: The power factor of the resonating circuit is unity.

At resonance, the inductive reactance (XL) and capacitive reactance (XC) are equal and opposite, resulting in their cancellation. This leads to a situation where the circuit behaves as if it is purely resistive. In a purely resistive circuit, the voltage and current are in phase, meaning the power factor is unity (PF = 1). Therefore, both series and parallel resonant circuits have a power factor of unity at resonance.

Additional Information

To further understand the analysis, let’s evaluate the other options:

Option 1: The power factor of the resonating circuit is zero.

This option is incorrect because the power factor of a resonating circuit is not zero. A power factor of zero would imply that the circuit is purely reactive (either inductive or capacitive), with no real power being consumed. At resonance, the circuit is purely resistive, and the power factor is unity, not zero.

Option 3: The impedance of the resonating circuit is minimum.

This option is partially correct but only applies to series resonant circuits. In a series resonant circuit, the impedance is minimized at the resonant frequency. However, in a parallel resonant circuit, the impedance is maximized at resonance. Therefore, this option does not capture the similarity between both series and parallel resonance.

Option 4: The current through the resonating circuit is maximum.

This option is also partially correct but again only applies to series resonant circuits. In a series resonant circuit, the current is maximum at the resonant frequency due to the minimized impedance. In a parallel resonant circuit, the current through the branches is maximum, but the overall current drawn from the source is minimized. Hence, this option does not apply to both types of resonance in the same way.

Conclusion:

Understanding the characteristics of series and parallel resonant circuits is essential for correctly identifying their operational similarities and differences. At resonance, both types of circuits exhibit a unity power factor, meaning the voltage and current are in phase, and the circuit behaves purely resistively. This key similarity makes option 2 the correct choice. Other options, while partially correct in specific contexts, do not capture this fundamental similarity between series and parallel resonance.